Key B battery is probably dead since it won't unlock/lock and why it would start the car.

Key A has a good battery but the EWS transponder thing is probably bad. happened to me. first thing was to try and get the key to communicate with the car again. forgot how to do it (google it) but it's something like holding the lock button for a certain time, putting the key in the ignition, etc, etc. if that doesn't work, you'll have to probably get a new key and sync it up.

What are these instructions you speak of having the key to talk to the car? I have never heard of that.. I only know of that syncing procedure.